REALIZACIÓN DE PRODUCTO

3.8.2.1 Flexible parametric survival models

To investigate the association of clinical factors and therapeutic strategies with improvements in survival following STEMI, Royston-Parmar flexible parametric survival models (132) were adopted for the survival analysis. These models fall under the parametric time to event modelling approach but instead of assuming the baseline hazard function follows a pre-defined distribution, flexible parametric models model the shape of the baseline hazard using restricted splines(132). This allows for flexibility in the shape but restricts the function to be linear on the ends were the data is sparse(132). The conventional survival modelling approach Cox PH modelling was not employed due to the violation of the proportional hazards assumption. The primary outcome of interest was one year survival and the exposure of interest was year of admission to hospital.

The covariates that were included in the survival models comprised: patient demographics (age, sex, deprivation (2010 IMD score), cardiovascular risk factors (diabetes, hypercholesterolaemia, hypertension, smoking status, COPD, family history of coronary heart disease, chronic renal failure, chronic cardiac failure), cardiovascular history (cerebrovascular disease, peripheral vascular disease, previous angina, previous AMI, previous PCI, previous CABG), hospital discharge medications (statins, aspirin, P2Y12 inhibitors, ACEi)/ARBs), year of admission to hospital, reperfusion (dichotomised to received PPCI or not) and cardiac rehabilitation. The discharge medication variables had to be included in the models as binary (receipt: yes/no), as including them as three level categorical variables (receipt: yes/no/contraindicated) was biasing the analysis in such a way that change in contraindication over time as well as prescription of the drugs was being captured. As a result masking the change in the prescription of the secondary drugs over time, of which this was one of the exposures of interest.

including the following categories of variables individually (as well as year of admission) : reperfusion, comorbidities and risk factors, cardiac rehabilitation, aspirin at discharge, statin at discharge, P2Y12 inhibitors at discharge, ACEi/ARBs at discharge, β-blockers at discharge and all the hospital discharge drugs (together rather than individually). Change in temporal trend by year was noted after addition of these categories of variables. To these nine models age, sex and IMD scores (demographics) were added and change in temporal trend was also noted after addition of these three variables. The final model then included all the considered variables. This pattern of adding variables to the model was followed in order to map out how the category of variables being added to the model affected temporal changes in one year survival. The flexible parametric models were fitted using the stpm2 command for each imputation, and model estimates combined using Rubin’s rules via the mi estimate command. The analysis was repeated but focusing on the secondary outcome, six month survival.

3.8.2.2 Mediation analysis

As a sensitivity analysis, mediation analysis was carried out to investigate the causal mechanisms by examining the role of the potential mediators (determined through flexible parametric modelling) thought to lie on the causal pathway between year of admission of the STEMI patients and survival (one year (primary outcome) and six months mortality). A mediating variable is a variable that appears on the causal pathway of an exposure outcome relationship (post-treatment variable that occurs before the outcome happens(133)) for example the variable M shown in Figure 3.7 is a mediator as it lies on the causal pathway between exposure T and outcome Y(134). Mediation analysis falls under the Structural Equation Modelling (SEM) framework and the illustration of mediation analysis given in this section follow that as in Linden et al.(134).

Figure 3.7 The conceptual mediation model with a single mediator.

where T: is treatment assignment. M: is the mediating variable Y: is the outcome

a,b,c’: represent the SEM coefficients.

The mediating variable (M) explains the relationship between the dependent (T) and the independent variable (Y) . However it’s not always the case that the mediator explains 100% of the relationship as there maybe other unmeasured mediators, such that the total treatment effects are the sum of both the direct (c) and indirect effects (a+b). The direct and indirect effects are quantified as illustrated by the equations below:

Y𝑖 = 𝛼1+ 𝑐T𝑖+ 𝛽1X𝑖 + 𝜀𝑖 3.2

M𝑖 = 𝛼2+ 𝑎T𝑖 + 𝛽2X𝑖 + 𝜀𝑖 3.3

Y_𝑖 = 𝛼₃+ 𝑏M_𝑖 + 𝑐′_𝑇

Equation 3.3 represents the a pathway in Figure 3.7 in which M (mediating variable) is regressed on T (treatment variable) and X (pre-treatment covariates)(134). All the equations were adopted from Linden et al.(134) Equation 3.4 represents both the b and c’ pathways shown in Figure 3.7 which regress Y (outcome variable) on T (treatment variable), M (mediating variable) and X (pre-treatment covariates).

After modelling as shown in the equations, the mediated effects can be estimated using the “product of coefficients” approach or “difference in coefficients” approach. The “product of coefficients” approach uses the product of a and b paths to quantify the indirect effects (mediated effects) and the “difference in coefficients” subtracts the direct effects c’ from the total effects c(135, 136). The total effect can also be quantified by adding the indirect and direct effects (c=ab+c’).The advantage of using mediation analysis is that it not only gives point estimates of the mediation, but also the extent to which a variable mediates a relationship(134). The mediated effects are derived as a ratio of the indirect to the total direct effect and quantified as a percentage(134). The estimation described so far is for a single mediator model and in the event of multiple mediators, each mediator is regressed individually on the treatment (including pre-intervention characteristics) and then the outcome model regresses the outcome (Y) on all the mediators as well as on T and X(134).

The SEM approach described above utilizes the ordinary least squares regression with the assumption that the mediator and outcome variables are continuous, however for the thesis the outcome and potential mediators were binary hence an approach that is suitable for binary outcomes and mediators was needed. For the purpose of this thesis the mediation analysis was carried out using the R package; mediation(137). This R mediation package accommodates a larger class of statistical models but still based

on model-based causal mediation analysis under the assumption of sequential ignorability similar to the SEM approach(137). This is achieved through the mediate function(137). The mediation analysis was undertaken following a two-step approach represented by equations 3.2 and 3.3. A logistic regression model for the mediating models (equation 3.3) was fitted, as the potential mediators were binary. For the outcome models (equation 3.2), a Poisson regression modelling framework with log survival time as the offset was used. The Poisson modelling approach was undertaken as to the best of my knowledge there were no software packages available to fit flexible parametric survival models for mediation analysis).

The potential pre-treatment covariates that were used for the analyses include; age, IMD score, sex, previous history of AMI, angina, previous CABG, diabetes, hypertension, peripheral vascular disease, a family history of coronary heart disease, COPD/asthma, hypercholesterolaemia, and previous coronary revascularisation, chronic renal failure, elevated cholesterol, current or ex-smoker status, and cardiac rehabilitation. In addition to these covariates in the outcome model the discharge medications (aspirin, β blockers, ACEi/ARBs and statins) not determined as potential mediators.

The analyses were undertaken for the primary outcome one year mortality and secondary outcome six month mortality. Average Direct Effects (ADE) (represented by c’ in Figure 3.7) and Average Causal Mediation Effects (ACME) (represented by paths a and b) were derived to quantify the percentage mediated by the potential mediator. The ACME and ADE are estimated under the potential outcomes framework whereby the impact of the mediator on the outcome is quantified comparing impact on outcomes if everyone in the population received treatment/mediating variable vs. if no one in the population received treatment/mediating variable(133). The potential outcomes come into play in the sense that not everyone has an

concluded if the sequential ignorability assumption is not violated(134). The mediation analysis was only conducted on the complete STEMI cases only (n=82,637).